Michael,
There is no law that says we have to agree on the words we use.
But in order to communicate effectively and to avoid confusion,
both among ourselves and among the people we're talking to, it
is essential to use words in the same or approximately the same
senses as well established usage.
> It only becomes an issue if we all have to agree on names, but
> that is unlikely to happen any time soon.
If we are hoping to establish any kind of standards for ontology
and related fields, we had better start by agreeing among ourselves.
And it helps if we're consistent with common usage.
Following is established usage in mathematics and logic:
The word 'set' is always defined by extension (i.e., two sets
with the same instances are the same; otherwise, different).
Following is established usage, as attested by dictionaries such
as the OED, Merriam-Webster, and any other you're likely to find:
The words 'category' and 'type' are defined by intension (i.e.,
common properties, qualities, or descriptions, independent of
the existence or nonexistence of any instances).
The word 'class', however, is ambiguous because it has different
definitions in various fields. In mathematics and logic, it is
often used as a synonym for 'set' or for a supertype of 'set'
that includes collections that are too big to be a proper set.
But the word 'class' also has ties to the verb 'classify', which
is usually used for classification by common properties. Therefore,
the word 'class' is sometimes used as a synonym for 'type'.
We had a debate about these issues on ontolog forum over a year ago,
and the consensus that emerged is the following:
1. 'set' is consistently used in an extensional sense.
2. 'type' is consistently used in an intensional sense.
3. But 'class' is ambiguously used in either the meaning of 'set'
or the meaning of 'type'. Therefore, any use of the word 'class'
is likely to create confusion, especially in a multidisciplinary
field, such as ontology.
In short, if you want to be clear and precise, use the words 'set'
and 'type'. But if you use the word 'class', you're likely to create
confusion.
John